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个人简介
My current work focuses on the mathematical theory of machine learning and integrating machine learning with multi-scale modeling.
Research summary: My work draws inspiration from various disciplines of sciences and has made an impact in fluid dynamics, chemistry, material sciences, and soft condensed matter physics. I have contributed to the resolution of some long standing scientific problems such as the Burgers turbulence problem (which was the original motivation of Burgers for proposing the well-known Burgers equation), the Cauchy-Born rule for crystalline solids (which indeed dates back to Cauchy, and provides a microscopic foundation for the elasticity theory), and the moving contact line problem (which is still largely open). A common theme is to try bringing clarity to scientific issues through mathematics. A second theme is multi-scale and/or multi-physics problems. I have also worked on building the mathematical framework and finding effective numerical algorithms for modeling rare events which is a very difficult class of problems involving multiple time scales (string method, minimum action methods, transition path theory, etc). I have also worked on multiscale analysis and algorithms (e.g. the heterogeneous multi-scale method) for stochastic simulation algorithms, homogenization problems, problems with multiple time scales, complex fluids, etc. My book (Principles of Multi-Scale Modeling, Cambridge Univ Press) provides a broad introduction to this subject. A third theme is to develop and analyze algorithms in general. In computational fluid mechanics, I was involved in analyzing and developing vorticity-based methods, the project method and the gauge method. In density functional theory (DFT), my collaborators and I have developed the PEXSI algorithm, which is so far the most efficient algorithm for DFT.
Research summary: My work draws inspiration from various disciplines of sciences and has made an impact in fluid dynamics, chemistry, material sciences, and soft condensed matter physics. I have contributed to the resolution of some long standing scientific problems such as the Burgers turbulence problem (which was the original motivation of Burgers for proposing the well-known Burgers equation), the Cauchy-Born rule for crystalline solids (which indeed dates back to Cauchy, and provides a microscopic foundation for the elasticity theory), and the moving contact line problem (which is still largely open). A common theme is to try bringing clarity to scientific issues through mathematics. A second theme is multi-scale and/or multi-physics problems. I have also worked on building the mathematical framework and finding effective numerical algorithms for modeling rare events which is a very difficult class of problems involving multiple time scales (string method, minimum action methods, transition path theory, etc). I have also worked on multiscale analysis and algorithms (e.g. the heterogeneous multi-scale method) for stochastic simulation algorithms, homogenization problems, problems with multiple time scales, complex fluids, etc. My book (Principles of Multi-Scale Modeling, Cambridge Univ Press) provides a broad introduction to this subject. A third theme is to develop and analyze algorithms in general. In computational fluid mechanics, I was involved in analyzing and developing vorticity-based methods, the project method and the gauge method. In density functional theory (DFT), my collaborators and I have developed the PEXSI algorithm, which is so far the most efficient algorithm for DFT.
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CoRR (2024)
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CoRR (2024)
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Communications on Applied Mathematics and Computationpp.1-28, (2024)
Proceedings of the National Academy of Sciences of the United States of Americano. 14 (2024): e2308668121-e2308668121
COMBUSTION AND FLAME (2024): 113286
Han Wang,Duo Zhang, Xinzijian Liu,Xiangyu Zhang, Chengqian Zhang,Chun Cai, Hangrui Bi, Yiming Du, Xuejian Qin, Jiameng Huang, Bowen Li, Yifan Shan,
crossref(2024)
Angewandte Chemie (International ed. in English)pp.e202405379-e202405379, (2024)
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